RT-APNN for Solving Gray Radiative Transfer Equations
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913848613666816 |
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| author | Xie, Xizhe Chen, Wengu Ma, Zheng Wang, Han |
| author_facet | Xie, Xizhe Chen, Wengu Ma, Zheng Wang, Han |
| contents | The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_14144 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | RT-APNN for Solving Gray Radiative Transfer Equations Xie, Xizhe Chen, Wengu Ma, Zheng Wang, Han Computational Physics The Gray Radiative Transfer Equations (GRTEs) are high-dimensional, multiscale problems that pose significant computational challenges for traditional numerical methods. Current deep learning approaches, including Physics-Informed Neural Networks (PINNs) and Asymptotically Preserving Neural Networks (APNNs), are largely restricted to low-dimensional or linear GRTEs. To address these challenges, we propose the Radiative Transfer Asymptotically Preserving Neural Network (RT-APNN), an innovative framework extending APNNs. RT-APNN integrates multiple neural networks into a cohesive architecture, reducing training time while ensuring high solution accuracy. Advanced techniques such as pre-training and Markov Chain Monte Carlo (MCMC) adaptive sampling are employed to tackle the complexities of long-term simulations and intricate boundary conditions. RT-APNN is the first deep learning method to successfully simulate the Marshak wave problem. Numerical experiments demonstrate its superiority over existing methods, including APNNs and MD-APNNs, in both accuracy and computational efficiency. Furthermore, RT-APNN excels at solving high-dimensional, nonlinear problems, underscoring its potential for diverse applications in science and engineering. |
| title | RT-APNN for Solving Gray Radiative Transfer Equations |
| topic | Computational Physics |
| url | https://arxiv.org/abs/2505.14144 |